SUMMER ASSIGNMENT FOR FUNCTIONS/TRIGONOMETRY Bring to school the st d of clss! This summer ssignment is designed to prepre ou for Functions/Trigonometr. Nothing on the summer ssignment is new. Everthing is review of topics students lerned in Alger I & II nd Geometr. If ou wnt to e successful during Functions/Trig, ou must e le to understnd nd ppl this informtion throughout net er. The ssignment m e completed with nother student ut e certin tht YOU understnd how to complete ever prolem. The nswers re ville online through GroupFusion. Be sure to check ever prolem. Netl show ll work for ech prolem, using pencil. Clcultors re onl necessr for #8, nd should not e relied upon for the reminder of the ssignment. During the second week of school, ou will hve test covering ll of the mteril from the summer ssignment. If ou need to review these topics or see emples, we recommend the wesite www.purplemth.com/modules/inde.htm, which lists mn Alger review topics. If, fter reviewing, ou need further ssistnce, plese e-mil Mr. Dougls t douglrp@pwcs.edu, Mr. Keskel t KESKELK@pwcs.edu, Mr. Bicknell t BickneHC@pwcs.edu, or Mrs. Gellios t gelliosj@pwcs.edu, with questions. Properties of Eponents: n m n n m n mn 0 mn PurpleMth Topics: Beginning Alger Topics: Eponents: Bsic Rules Negtive Eponents Simplifing with Eponents Simplif the following epressions using the properties ove. Leve no negtive eponents.. 4w. 64 p 8. w w 7 64 6. 80 t. 4. z 4 0 0 6 6 z 7. 4 4 8 z
Rtionl Eponents: n m m n PurpleMth Topics: Beginning Alger Topic: Eponents: Frctionl Eponents Simplif the following epressions using the propert ove. Epress rdicls s frctionl eponents. 8. m 0. t 9. 4 n. 6 Comple Numers: i PurpleMth Topic: Advnced Alger Topics: Comple Numers Simplif the following epressions using imginr numers.. 4. i. 8 Qudrtic Formul: 4c PurpleMth Topic: Intermedite Alger Topics: Qudrtic Formul Solve the following qudrtic equtions using the qudrtic formul. Simplif s much s possile.. 7. 4w w 6 6. c c 7 0
Fctoring: Alws look for gretest common fctor first: Perfect Squre Trinomils: or Difference of Squres: Sum of Cues: Difference of Cues: PurpleMth Topics: Beginning Alger Topics: Simple Fctoring Intermedite Alger Topics: Fctoring Qudrtics Solving Qudrtic Equtions Specil Fctoring Formuls Solve the following equtions using fctoring. Show fctored eqution nd give ll solutions rel nd imginr. 8. 4 4 7 0. 6 0 9. 9 0 4. p p p 0 0. 6 0. p 9p 90 0. 9 4 0 6. 6 0. 09 0 7. 4n 78n 0
Pthgoren Theorem: c Solve for the unknown in ech of the figures elow. Give nswers ccurte to four deciml plces. 8. 9. in. PurpleMth Topic:...nd the eginnings of trig: Pthgoren Theorem ft 4 ft 4 in. Trigonometr: sin cos tn opposite hpotenuse djcent hpotenuse opposite djcent PurpleMth Topic:...nd the eginnings of trig: Bsic Trigonometric Rtios Inverses of Trigonometric Rtios Specil Angle Vlues Use the following right tringles to find the vlue of the unknown. Give nswers ccurte to four deciml plces. 0.. m p 9 d 6.. 7 mm z cm r 68 cm
Lines: slope: m midpoint:, eqution of line: m PurpleMth Topics: Beginning Alger Topics: Slope of Stright Line Midpoint Formul Stright-line Equtions For ech of the following sets of points, find: the slope the eqution of the line tht fits these points c the midpoint 4., 8 6, 0., 4 0, 8 6. 0, 4 0,
Epnd the following epressions. 7. 8 8. 4 Simplif the following rtionl functions. Stte n restrictions. 9. 4 6 40. 9 8 9 8 8 6 4. 8 6 6 4. 4. Rtionl Epressions: 0 0, 0,,, r s q where r s q p f then s r q p f If Binomil Epnsion: PurpleMth Topic: Beginning Alger Topics: Polnomils: Multipling PurpleMth Topics: Advnced Alger Topics: Rtionl Epressions: Simplifing Rtionl Epressions: Adding Rtionl Epressions: Multipling Comple Frctions
Grphing: Chnges to the outside of f ffect grph verticll. Chnges to the inside of f ffect grph horizontll. Domin is the set of possile -vlues. Rnge is the set of possile -vlues. PurpleMth Topics: Intermedite Alger Topics: Domin nd Rnge Grphing Qudrtic Equtions Grph the following functions. Stte the domin nd rnge of ech. 44. f 46. f 4. f 4
Sstems of Equtions: The solution to sstem of equtions, f, g is the point of intersection,,, of the functions. 47. Solve the sstem using sustitution: 4 + = 9 = 4 PurpleMth Topics: Advnced Alger Topics: Solving Sstems of Liner Equtions Sections: Sustitution p. 4 Elimintion/ddition p. 48. Solve the sstem using elimintion: m n = - m + n = 0 Common Mistkes in Alger Decide whether ech of the following simplifictions is ccurte. If it is not, correct the right side of the eqution to mke it true. 49. 9. 4 4 4 0. 4. 6. - 4 6.. + 4 7 6. 4
7. 4 6. 8. 64. 9. 4 6. 4 0 60. 66. 0 0 4 6. 67. 6. 68. 4
69. 70. 6 8 4 7. 4 7. w z z w